科研之友
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摘要
Let k be a perfect field of characteristic p, X-i (i = 1, 2) smooth k-schemes, fi : X-i -> A1/k two k-morphisms of finite type, and f : X-1 x(k) X-2 -> A1/k the morphism defined by f(z(1), z(2)) = f(1)(z(1)) + f(2)(z(2)). For each i is an element of {1, 2}, let x(i) be a k-rational point in the fiber f(i)(-1)(0) such that f(i) is smooth on X-i - {x(i)}. Using the l-adic Fourier transformation and the stationary phase principle of Laumon, we prove that the vanishing cycles complex of f at x = (x(1), x(2)) is the convolution product of the vanishing cycles complexes of f(i) at x(i) (i = 1, 2).
- 出版日期2014
- 单位南开大学
